Is this a grammatically correct way to show equivalence?

Question

$$ \frac{1}{k} - \frac{1}{k+1} > \frac{1}{(k+1)^2} \iff \frac{1}{k(k+1)} > \frac{1}{(k+1)(k+1)} $$

Im just trying to figure out if I've used the '$\iff$' correctly. Thanks in advance.

Answer 1

Yes, you use the symbol $\iff$ correctly. $A \iff B$ means that $A$ is true if and only if $B$ is true. Ti check that a $A \iff B$ hold true, one often breaks it into two directions $A \Rightarrow B$ and $A \Leftarrow B$. That is, you assume that $A$ is true and the you assume that $B$ is true. And after that, you assume that $B$ is true and prove that $A$ is true.